HARMONIC ANALYSIS AND PREDICTION OF TIDES 765) 
+eos (b¢+ 8) cos = oe sin (b¢+ 8) sin eG sayy 
+cos (bt+ B) cos (3 ore) — sin (bt+ 8) sin (3 ne) 
360bp 
a 
+2 co s 2 200? + 9 cos uly cos (bt-+ 8) 
== On ible) E +2 cos 
sin 2 Belle cos OU 
2 
=1F\F,B\ 2 sia AE a ae cos (bt-+ 8) 
sin -——— 
i 1260bp 
a 
a 
220. Replacing the equivalents of F; and F, in (313), the average 
value of the B ordinate as obtained by the secondary summations 
may be written 
sin 126060 
24a : Fin OD |” cos (bt+ 8) (814) 
mpb~ 
—o 
7 sin 
Since the true ordinate of constituent B at any time ¢ is equal to 
B cos (bt+ 8), the reciprocal of the bracketed coefficient will be the 
augmenting factor necessary to reduce the B ordinate as obtained 
from the summations to their true values. 
This augmenting factor may be written 
180bp 
arbp wp’ [7 sin ; 
24a sin uu 24 sin — | sin 126060 (315) 
a 
The first factor of the above is to be omitted if the primary sum- 
mations are for constituent S. It will be noted that the middle factor 
is the same as the augmenting factor that would be used if constituent 
B had been subjected to the primary summations. 
PHASE LAG OR EPOCH 
221. The phase lag or epoch of a tidal constituent, which is repre- 
sented by the Greek kappa (x), is the difference between the phase of 
the observed constituent and the phase of its argument at the same 
time. This difference remains approximately constant for any con- 
stituent in a particular locality. The phase of a constituent argument 
for any time may be obtained from the argument formula in table 2 by 
making suitable substitutions for the astronomical elements. The 
argument itself is represented’ by the general symbol (V-+-u) or E and 
